Weird mesh deformation for hollow object
As Monolith said, it means than some other bones have influence on this part of the mesh.

The easiest way to fix it is to select this part of the mesh in Edit mode, then go in the Properties panel > Data > Vertex Groups, and in the menu on the right of the vertex groups list, click on Remove From All Groups so that the vertices you've selected won't be part of any group anymore, and won't be controlled by any bone.

Now keep the vertices selected, in the vertex groups list select the group these vertices are supposed to be part of (i.e. group that has the name of the head bone) and click on the Assign Button.

Or to assign you can also switch your armature to Pose mode, select the object, switch to Weight Paint mode, select the head bone (it should be blueish), then paint with the brush (Mix option).